Electronic Journal of Probability

Shape theorem and surface fluctuation for Poisson cylinders

Marcelo Hilario, Xinyi Li, and Petr Panov

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We prove a shape theorem for Poisson cylinders, and give a power-law bound on surface fluctuations. In particular, we show that for any $a \in (1/2, 1)$, conditioned on the origin being in the set of cylinders, if a point belongs to this set and has Euclidean norm below $R$, then this point lies at internal distance less than $R + O(R^{a})$ from the origin.

Article information

Electron. J. Probab., Volume 24 (2019), paper no. 68, 16 pp.

Received: 27 July 2018
Accepted: 28 May 2019
First available in Project Euclid: 28 June 2019

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Primary: 60F10: Large deviations 82B43: Percolation [See also 60K35] 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 51F99: None of the above, but in this section

Poisson cylinder model internal distance shape theorem

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Hilario, Marcelo; Li, Xinyi; Panov, Petr. Shape theorem and surface fluctuation for Poisson cylinders. Electron. J. Probab. 24 (2019), paper no. 68, 16 pp. doi:10.1214/19-EJP329. https://projecteuclid.org/euclid.ejp/1561687601

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